51–60 of 86 posts
Again with the Ramsey theory! Every day, i'm reading about some amazing new result in Ramsey theory! It's like the microservices of discrete mathematics! Enough already!
"Maximum numbers of cards that would have no SET in an n-attribute version of the SET card game"
The OEIS links appear to have been updated to reflect the recent breakthrough of Ellenberg and Gijswijt, including their unified paper arXiv:1605.09223 from May 30.
Earlier quoted context omitted.
Building on research seems like it's a form of peer review, especially in math where you'd need to understand the entire proof before making incremental improvements to it.
While this can be true it's also common to have "assuming X is true" where X is some very complicated hypothesis. We saw this with Fermat's Last Theorem and it was with a great sigh of relief that it was finally proven in the 90s. If the inverse was true then entire fields of Mathematics would have collapsed.
For a real good example see https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...
> The paper soon set off a cascade of what Ellenberg called “math at Internet speed.” Within 10 days, Ellenberg and Dion Gijswijt, a mathematician at Delft University of Technology in the Netherlands, had each independently posted papers showing how to modify the argument to polish off the original cap set problem in just three pages. This is a very interesting trend I've noticed. I wanted to cite a few papers on arX…
I would argue that this is a dangerous claim, because an algorithm working generally is different from proof that it always works, and this can lead to serious issues. I would say that this is one of the big reasons peer review exists!
Earlier quoted context omitted.
Our friend is so jarringly good at Set and Scrabble that nobody will play with her anymore. She has to play people on the internet and they frequently disconnect mid-match.
If you want to lose friends and be disowned from your family - learn to play Monopoly by the actual rules and follow this strategy: http://imgur.com/a/vX3zm I can confirm that it works and nobody wants to play Monopoly anymore. Instead we play more fun board games
I don't understand the Alice imagery (nor the witch, not sure if that is also Alice imagery somehow) -- any ideas?
2 4 9 20 45 112
Earlier quoted context omitted.
> If the inverse was true then entire fields of Mathematics would have collapsed. Honest question: what would've been the consequences of this?
The consequence is that a whole body of work winds up coming with an asterisk until people figure out what they can and can't trust. Papers may be looked at for inspiration, but won't be quoted for results. Eventually some of it gets proved properly, and the rest is abandoned. After that the older papers become mere historical curiosities. A reasonably recent example of this is the https://en.wikipedia.org/wiki/Itali…
Earlier quoted context omitted.
Funny anecdata: in my circle of friends, the trait that best predicts Set skill isn't IQ or gender or anything like that, it's musical ability. This came up at a party. Six people playing Set, all of us from different cities, and the three that took band in high school utterly dominated the three that didn't. The reason? Field trips. The Band kids had all played Set for hours on buses, the rest of us had only played…
I like how you introduce a correlating attribute in the beginning of your comment, get me thinking about the relationship between musical ability and set-identifying ability, then clobber whatever hypothesis I was putting together just as fast with the confounding "field trips" variable. Nice work :)